Increase or decrease vertices in circle after working with it?
For the creation of a primitive

Yes, and no
You can change the settings right after creating any of the primitives, by pressing f6.
After you do anything else, (besides moving around the view) the settings are gone with no way to get back to them.

Editing loop count in a circle

To reduce the number of edges.
In edit mode, select every other loop by Alt RMB  (use shift to add to the selection). Then press X or delete and choose Edge Loop. Do the same for the edges on the other axis.

  

To increase the number of edges.
Delete the bottom and top vertex (where all the loops meet). Select everything with A, then press W and choose Subdivide Smooth. The loops will get wavy, to fix that select them with Alt RMB  then press S Z 0. Which will flatten them along the Z axis. 

To fix the holes in the top of the circle, select the top edge loop, and extrude it along the Z axis. Then scale to 0, and remove doubles. Do the same for the bottom of the circle.